Maxwell's methodology of estimating effective properties: Alive and well

I. Sevostianov; S. G. Mogilevskaya; V. I. Kushch

doi:10.1016/j.ijengsci.2019.05.001

Maxwell's methodology of estimating effective properties: Alive and well

I. Sevostianov, S. G. Mogilevskaya, V. I. Kushch

Civil, Environmental, and Geo- Engineering

Research output: Contribution to journal › Review article › peer-review

55 Scopus citations

Abstract

This paper presents a comprehensive review of the far-field-based methodology of estimation of the effective properties of multi-phase composites that was pioneered by Maxwell in 1873 in the context of effective electrical conductivity of a particle-reinforced material. Maxwell suggested that a cluster of particles embedded in an infinite medium subjected to a uniform electrical field has the same far-field asymptotic as an equivalent sphere whose conductivity is equal to the effective one; this yields closed-form formula for the effective conductivity. Our review focuses on subsequent developments of Maxwell's idea in various applications and on its range of applicability. The conclusion is that, 145 years later, the methodology is still alive and well.

Original language	English (US)
Pages (from-to)	35-88
Number of pages	54
Journal	International Journal of Engineering Science
Volume	140
DOIs	https://doi.org/10.1016/j.ijengsci.2019.05.001
State	Published - Jul 2019

Bibliographical note

Funding Information:
The first author (I.S.) gratefully acknowledges support from NIH Clinical Center grant 2R25GM061222-18 to NMSU. The second author (S.M.) gratefully acknowledges support from the Theodore W. Bennett Chair, University of Minnesota. The third author (V.K.) acknowledges support from the Science and Technology Center in Ukraine through the Grant #6247 .

Publisher Copyright:
© 2019 Elsevier Ltd

Keywords

Composite materials
Effective properties
Maxwell's methodology

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10.1016/j.ijengsci.2019.05.001

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abstract = "This paper presents a comprehensive review of the far-field-based methodology of estimation of the effective properties of multi-phase composites that was pioneered by Maxwell in 1873 in the context of effective electrical conductivity of a particle-reinforced material. Maxwell suggested that a cluster of particles embedded in an infinite medium subjected to a uniform electrical field has the same far-field asymptotic as an equivalent sphere whose conductivity is equal to the effective one; this yields closed-form formula for the effective conductivity. Our review focuses on subsequent developments of Maxwell's idea in various applications and on its range of applicability. The conclusion is that, 145 years later, the methodology is still alive and well.",

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AU - Kushch, V. I.

N1 - Funding Information: The first author (I.S.) gratefully acknowledges support from NIH Clinical Center grant 2R25GM061222-18 to NMSU. The second author (S.M.) gratefully acknowledges support from the Theodore W. Bennett Chair, University of Minnesota. The third author (V.K.) acknowledges support from the Science and Technology Center in Ukraine through the Grant #6247 . Publisher Copyright: © 2019 Elsevier Ltd

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N2 - This paper presents a comprehensive review of the far-field-based methodology of estimation of the effective properties of multi-phase composites that was pioneered by Maxwell in 1873 in the context of effective electrical conductivity of a particle-reinforced material. Maxwell suggested that a cluster of particles embedded in an infinite medium subjected to a uniform electrical field has the same far-field asymptotic as an equivalent sphere whose conductivity is equal to the effective one; this yields closed-form formula for the effective conductivity. Our review focuses on subsequent developments of Maxwell's idea in various applications and on its range of applicability. The conclusion is that, 145 years later, the methodology is still alive and well.

AB - This paper presents a comprehensive review of the far-field-based methodology of estimation of the effective properties of multi-phase composites that was pioneered by Maxwell in 1873 in the context of effective electrical conductivity of a particle-reinforced material. Maxwell suggested that a cluster of particles embedded in an infinite medium subjected to a uniform electrical field has the same far-field asymptotic as an equivalent sphere whose conductivity is equal to the effective one; this yields closed-form formula for the effective conductivity. Our review focuses on subsequent developments of Maxwell's idea in various applications and on its range of applicability. The conclusion is that, 145 years later, the methodology is still alive and well.

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Maxwell's methodology of estimating effective properties: Alive and well

Abstract

Bibliographical note

Keywords

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